Vortia 3DHow Vortia 3D calculates
Published on by Raul Rodríguez
Which formulas the app uses, where the coefficients come from and what is left for you to check. So you know what lies behind every number in the report.
1. The air
Density and viscosity are calculated from the project temperature and altitude:
p = 101,325 · (1 − 2.25577·10⁻⁵·h)^5.25588 · ρ = p / (287.05 · T) · μ = 1.458·10⁻⁶ · T^1.5 / (T + 110.4)ISA standard atmosphere, ideal gas and Sutherland’s law (T in K, h in m)At 20 °C and sea level this gives 1.204 kg/m³ and 1.506·10⁻⁵ m²/s. At 1,000 m altitude the density drops by 11 %, and all the pressure losses with it.
2. Duct friction
Δp = f · (L / Dh) · ρ·v² / 2 · 1/√f = −2·log₁₀( ε/(3.7·Dh) + 2.51/(Re·√f) )Darcy-Weisbach with Colebrook-White, solved iteratively (starting from Swamee-Jain). With Re < 2,300, f = 64/Re.- Roughness ε (ASHRAE): galvanised sheet steel 0.09 mm, fully extended flexible duct 0.91 mm, or the value you enter.
- Rectangular duct: velocity and velocity pressure come from the actual area a·b; friction from the hydraulic diameter Dh = 2ab/(a + b).
- Fittings too: the app adds the friction along the length of each component (the R·θ developed length of a bend, the body of a damper or a tee), not just in straight runs.
3. Fittings
Each fitting loses ζ·ρ·v²/2. The coefficients come from published tables:
| Component | Source and criterion |
|---|---|
| Circular bend | ASHRAE CD3-1: C at 90° by R/D (0.71 at R/D 0.5; 0.15 at 1.5) times the angle factor |
| Butterfly damper | ASHRAE CD9-1: 0.20 open, 4.5 at 30°, 29 at 50° |
| Reducer | Idelchik: abrupt ζ = 0.5·(1 − A₂/A₁)^0.75; conical ≤ 45° ≈ 0.05 |
| Expansion | Gibson (Idelchik): Δp = ψ(θ)·ρ(v₁ − v₂)²/2; at 180°, Borda-Carnot |
| Tees and Y-pieces | Idelchik: diverging on supply and converging on extract, according to the airflow split and the area ratio. Curved tee: 0.55 of the branch coefficient |
| Hoods | ACGIH: entry loss C·Pd (0.25 tapered, 0.50 booth, 0.93 plain opening) |
| Flow straighteners | ISO 5167-1, AMCA 210 and Idelchik (cross 0.15, star 0.25, honeycomb 0.75) |
| Filter or other equipment | The catalogue ΔP at its nominal airflow, scaled by (Q/Qn)² |
Coefficients refer to the velocity pressure of the duct. For tees, those of the common duct are used.
4. How the network is solved
The problem is not adding up losses: it is knowing how much air goes down each branch. The app solves it like this:
- Curves for each branch. From each terminal towards the fan, it calculates the pressure needed at each point to move any airflow to that terminal.
- Split at the tees. At each branch it finds the airflow split at which both branches require the same pressure at the junction. That is how the real network shares out the air if you do not balance it.
- Forward pass. With the fan airflow, it runs through the network and records, for each component, airflow, velocity, losses and total, static and velocity pressure.
- Closure. It checks that exactly the right pressure is left at each terminal (an error of a few hundredths of a pascal).
It then adds leakage (EN 12237: f = c·p^0.65 with the airtightness class and the pressure of each component), the system effect at the fan opening (AMCA 201) and the specific fan power SFP (EN 16798-3). If you paste the fan curve, it calculates the duty point by crossing it with the system curve, and the required frequency with the fan laws.
Automatic balancing closes the dampers on each branch until every terminal gets its airflow, leaving the one on the index branch open. Sizing chooses diameters from the EN 1506 series by velocity or by constant pressure drop.
5. Grilles and diffusers
With catalogue data, the app scales the pressure drop with the actual airflow: Δp = Δpn·(Q/Qn)². With the app’s generic catalogue:
Δp = ζ · ρ/2 · (Q / Aef)² · LwA = a + b·log v + 10·log AefEffective area by size; ζ, a and b fitted to ≈ 700 points from the tables of a Spanish manufacturerAccuracy of the fit: ±10 % in pressure drop and ±2–4 dB in noise. It is for preliminary sizing; for the final installation, the catalogue of the model installed takes precedence.
6. Noise in the rooms
ASHRAE octave-band method (63 Hz – 8 kHz), “Noise and Vibration Control”:
- Fan sound power. From its catalogue; if you do not have it, an empirical estimate: Lw = 20·log p + 10·log V + 40, with the typical axial or centrifugal spectrum.
- Network attenuation. Unlined straight duct, bends, sound power split at tees according to airflow, and end reflection at the terminal.
- Silencers. Insertion loss by band with Sabine’s formula for lined ducts, ΔL = 1.05·α1.4·P/S dB/m (50 or 100 mm absorbent, with or without a pod, or splitter type), with less attenuation at high frequencies when the airway is wide. With the manufacturer’s catalogue, its attenuation and its ΔP.
- Self-noise of terminals from the generic catalogue, added.
- From terminal to listener. Lp = Lw + 10·log(Q/(4πr²) + 4/R), with the typical room for each use. Result in dB(A) and NR curve.
- Limits of the Spanish noise regulation RD 1367/2007, table B2 (required by the Spanish Building Code CTE DB-HR and by RITE); in industrial buildings, RD 286/2006.
It does not include the noise generated by fittings and by the silencer itself, nor noise radiated by the duct walls.
7. Check against an example
The worked example from our guide to duct pressure drop (in Spanish): a Ø250 galvanised sheet steel branch, 1,000 m³/h, 12 m straight, 3 bends at R/D 1.5, an open damper and a 20 Pa diffuser. The same branch in the app:
| Item | By hand | Vortia 3D |
|---|---|---|
| Velocity · velocity pressure | 5.66 m/s · 19.2 Pa | 5.66 m/s · 19.3 Pa |
| Friction factor · pressure drop per metre | 0.020 · 1.53 Pa/m | 0.0199 · 1.54 Pa/m |
| 12 m of straight run | 18.4 Pa | 18.4 Pa |
| 3 bends (ζ = 0.15) | 8.6 Pa | 8.7 Pa |
| Open damper (ζ = 0.20) | 3.8 Pa | 3.9 Pa |
| Friction inside bends and damper (2.0 m) | — | 3.1 Pa |
| Diffuser | 20.0 Pa | 20.0 Pa |
| Branch total | 50.8 Pa | 54.1 Pa |
Air at 20 °C and sea level (ρ = 1.204 kg/m³). Difference: 3.3 Pa (6 %).
The figures match component by component. The difference lies in a detail that hand calculations usually leave out: the air also rubs along the inside of the bends (0.59 m developed length each at R/D 1.5) and of the damper. The app counts it; if you want to repeat it by hand, measure those metres as straight duct.
8. What the app checks and what is left to you
The app warns you about
- Velocities above those recommended for the use (Spanish CTE DB-HS 3 in dwellings, ASHRAE criteria in non-residential and industrial buildings) and, on extract, below the transport velocity (ACGIH).
- Terminals receiving more or less airflow than planned, and which damper to adjust.
- Negative static pressure on supply, branches larger than the main duct and non-standard sizes.
- Fittings too close to the fan (AMCA 201), leakage, specific fan power above the limit and duty point off the curve.
- Noise above the room limit and hoods that do not capture at the required velocity.
Every warning comes with its fix: “View component” highlights it in the list and in 3D, and the button next to it applies the fix (size, balance, add a damper or a silencer, remove a reducer that does not reduce…). Everything can be undone.
Minimum airflow rates: Spain or Europe
The room assistant calculates the minimum airflow of each room with the Spanish regulations (CTE DB HS 3 in dwellings, RITE elsewhere, RD 486/1997 in industrial buildings). For projects outside Spain, EN 16798-1 mode (Europe mode) uses EN 16798-1 Annex B: airflow per person plus airflow per m² according to the indoor air quality category (I–IV) and the building emissions, and in dwellings the total ventilation and the minimum kitchen and bathroom extract. In that mode the warnings, the report and the design report cite EN 16798-1 and present as recommendations anything without a European equivalent.
What the designer must check
- The real catalogue data of grilles, diffusers, filters and fan.
- The real silencer: that it provides at least the octave-band attenuation of the generic one, with its catalogue pressure drop.
- Fire protection (Spanish CTE DB-SI), supports, cleaning access (EN 15780) and, for dust extraction, ATEX.
- That the layout can actually be installed on site.
It is a one-dimensional calculation by runs, with incompressible and steady flow: the method of the ductwork design handbooks. The 3D view shows that result; it is not CFD.